Abstract:

We introduce the Clock-Aware Linear Temporal Logic (CA-LTL) for expressing linear time properties of timed automata, and show how to apply the standard automata-based approach of Vardi and Wolper to check for the validity of a CA-LTL formula over the continuous-time semantics of a~timed automaton. Our model checking procedure employs zone-based abstraction and a new concept of the so called ultraregions. We also show that the Timed Büchi Automaton Emptiness problem is not the problem that the intended automata-based approach to CA-LTL model checking is reduced to. Finally, we give the necessary proofs of correctness, some hints for an efficient implementation, and preliminary experimental evaluation of our technique.

Modal Process Rewrite Systems

Abstract:

We consider modal transition systems with infinite state space generated by finite sets of rules. In particular, we extend process rewrite systems to the modal setting and investigate decidability of the modal refinement relation between systems from various subclasses. Since already simulation is undecidable for most of the cases, we focus on the case where either the refined or the refining process is finite. Namely, we show decidability for pushdown automata extending the non-modal case and surprising undecidability for basic parallel processes. Further, we prove decidability when both systems are visibly pushdown automata. For the decidable cases, we also provide complexities. Finally, we discuss a notion of bisimulation over MTS.

Abstract:

Modal transition systems are a well-established specification formalism for a high-level modelling of component-based software systems. We present a novel extension of the formalism called modal transition systems with durations where time durations are modelled as controllable or uncontrollable intervals. We further equip the model with two kinds of quantitative aspects: each action has its own running cost per time unit, and actions may require several hardware components of different costs. We ask the question, given a fixed budget for the hardware components, what is the implementation with the cheapest long-run average reward. We give an algorithm for computing such optimal implementations via a reduction to a new extension of mean payoff games with time durations and analyse the complexity of the algorithm.

Parametric Modal Transition Systems

Abstract:

Modal transition systems (MTS) is a well-studied specification formalism of reactive systems supporting a step-wise refinement methodology. Despite its many advantages, the formalism as well as its currently
known extensions are incapable of expressing some practically needed aspects in the refinement process like exclusive, conditional and persistent choices.
We introduce a new model called parametric modal transition systems (PMTS) together with a general modal refinement notion that overcome many of the limitations and we investigate the computational complexity of modal refinement checking.

Abstract:

Modal transition systems (MTS) is a well established formalism used for specification and for abstract interpretation. We consider its disjunctive extension (DMTS) and we show that refinement problems for DMTS are not harder than in the case of MTS. There are two main results in the paper. Firstly, we give a solution to the common implementation and specification problems lowering the complexity from EXPTIME to PTIME. Secondly, we identify a fundamental error made in previous attempts at LTL model checking of MTS and provide algorithms for LTL model checking of MTS and DMTS. Moreover, we show how to apply this result to compositional verification and circumvent the general incompleteness of the MTS composition.

Process Algebra for Modal Transition Systemses

Abstract:

The formalism of modal transition systems (MTS) is a well established framework for systems specification as well as abstract interpretation. Nevertheless, due to incapability to capture some useful features, various extensions have been studied, such as e.g. mixed transition systems or disjunctive MTS. Thus a need to compare them has emerged.
Therefore, we introduce transition systems with obligations as a general model encompassing all the aforementioned models, and equip it with a process algebra description. Using these instruments, we then compare the previously studied subclasses and characterize their relationships.

Abstract:

Modal transition systems (MTS), a specification
formalism introduced more than 20 years
ago, has recently received a considerable attention in
several different areas.
Many of the fundamental questions
related to MTSs have already been answered. However,
the problem of the exact computational complexity of thorough refinement
checking between two finite MTSs remained unsolved.

We settle down this question by showing EXPTIME-completeness
of thorough refinement checking on finite MTSs.
The upper-bound result relies on a novel algorithm running
in single exponential time providing a direct goal-oriented
way to decide thorough
refinement. If the right-hand side MTS is moreover deterministic,
or has a fixed size, the running time of the algorithm becomes polynomial.
The lower-bound proof
is achieved by reduction from the acceptance problem of
alternating linear bounded automata and the problem remains EXPTIME-hard
even if the left-hand side MTS is fixed.

Partial Order Reduction for State/Event LTL

Abstract:

Software systems assembled from a large number of autonomous components become an interesting target for formal verification due to the issue of correct interplay in component interaction. State/event LTL incorporates both states and events to express important properties of component-based software systems.

The main contribution of the paper is a partial order reduction technique for verification of state/event LTL properties. The core of the partial order reduction is a novel notion of stuttering equivalence which we call state/event stuttering equivalence. The positive attribute of the equivalence is that it can be resolved with existing methods for partial order reduction. State/event LTL properties are, in general, not preserved under state/event stuttering equivalence. To this end we define a new logic, called weak state/event LTL, which is invariant under the new equivalence.